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Feature subset selection, as a special case of the general subset selectionproblem, has been the topic of a considerable number of studies due to thegrowing importance of data-mining applications. In the feature subset selectionproblem there are two main issues that need to be addressed: (i) Finding anappropriate measure function than can be fairly fast and robustly computed forhigh-dimensional data. (ii) A search strategy to optimize the measure over thesubset space in a reasonable amount of time. In this article mutual informationbetween features and class labels is considered to be the measure function. Twoseries expansions for mutual information are proposed, and it is shown thatmost heuristic criteria suggested in the literature are truncatedapproximations of these expansions. It is well-known that searching the wholesubset space is an NP-hard problem. Here, instead of the conventionalsequential search algorithms, we suggest a parallel search strategy based onsemidefinite programming (SDP) that can search through the subset space inpolynomial time. By exploiting the similarities between the proposed algorithmand an instance of the maximum-cut problem in graph theory, the approximationratio of this algorithm is derived and is compared with the approximation ratioof the backward elimination method. The experiments show that it can bemisleading to judge the quality of a measure solely based on the classificationaccuracy, without taking the effect of the non-optimum search strategy intoaccount.

A Semidefinite Programming Based Search Strategy for Feature Selection with Mutual Information Measure